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A criterion for the nonporosity of a general Cantor set. (English) Zbl 0723.26002

The author considers (under some assumptions) the relationship between the \(\sigma\)-porosity and porosity of a general Cantor set.
Reviewer: R.Pawlak (Łódź)

MSC:

26A03 Foundations: limits and generalizations, elementary topology of the line
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[1] E. P. Dolženko, Boundary properties of arbitrary functions, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 3 – 14 (Russian).
[2] P. D. Humke and B. S. Thomson, A porosity characterization of symmetric perfect sets, Classical real analysis (Madison, Wis., 1982) Contemp. Math., vol. 42, Amer. Math. Soc., Providence, RI, 1985, pp. 81 – 85. · doi:10.1090/conm/042/807980
[3] B. S. Thomson, Derivation bases on the real line. I, Real Anal. Exchange 8 (1982/83), no. 1, 67 – 207. B. S. Thomson, Derivation bases on the real line. II, Real Anal. Exchange 8 (1982/83), no. 2, 278 – 442. · Zbl 0525.26002
[4] Brian S. Thomson, Real functions, Lecture Notes in Mathematics, vol. 1170, Springer-Verlag, Berlin, 1985. · Zbl 0581.26001
[5] Luděk Zajíček, Sets of \?-porosity and sets of \?-porosity (\?), Časopis Pěst. Mat. 101 (1976), no. 4, 350 – 359 (English, with Loose Russian summary). · Zbl 0341.30026
[6] L. Zajíček, Porosity and \?-porosity, Real Anal. Exchange 13 (1987/88), no. 2, 314 – 350. · Zbl 0666.26003
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